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a\left(4a^{2}-b^{2}-2a-b\right)
Factor out a.
4a^{2}-2a-b^{2}-b
Consider 4a^{2}-b^{2}-2a-b. Consider 4a^{2}-b^{2}-2a-b as a polynomial over variable a.
\left(2a+b\right)\left(2a-b-1\right)
Find one factor of the form ka^{m}+n, where ka^{m} divides the monomial with the highest power 4a^{2} and n divides the constant factor -b^{2}-b. One such factor is 2a+b. Factor the polynomial by dividing it by this factor.
a\left(2a+b\right)\left(2a-b-1\right)
Rewrite the complete factored expression.